FIG. 1 illustrates a known example of a roller chain drive system 10 such as an automotive timing system. The chain drive system 10 includes a drive sprocket 12 and a driven sprocket 14. The system 10 further includes a roller chain 16 having a number of rollers 18 which engage and wrap about sprockets 12,14. The roller chain 16 is drivingly engaged with the sprockets 12,14, both of which rotate in a clockwise direction as shown by arrow 11.
The roller chain 16 has two spans extending between the sprockets 12,14; a slack strand 20 and taut strand 22. In the illustrated example, the sprocket 12 is a drive sprocket and the sprocket 14 is driven by the sprocket 12 by means of chain 16. As such, the roller chain 16 is under tension as shown by arrows 24. A central portion of the taut strand 22 is guided from the driven sprocket 14 to the drive sprocket 12 with a chain guide 26. A first roller 28 is shown fully seated at a twelve o'clock position on the drive sprocket 12. A second roller 30 is adjacent to the first roller 28 and is the next roller to mesh with the drive sprocket 12.
As is generally known, either sprocket 12,14 or both can be an ISO-606 compliant sprocket. For purposes of background only, an ISO-606 compliant sprocket tooth profile is disclosed in FIGS. 2A and 2B. The tooth space is defined by or comprises a continuous fillet or root radius Ri extending from one tooth flank (i.e., side) to the adjacent tooth flank as defined by the roller seating angle α. The flank radius Rf is tangent to the roller seating radius Ri at the tangency point TP. A chain with a link pitch P has rollers of diameter D1 in contact with the tooth spaces. The ISO sprocket has a chordal pitch also of length P, a root diameter D2, and Z number of teeth. The pitch circle diameter PD, tip or outside diameter OD, and tooth angle A (equal to 360°/Z) further define the ISO-606 compliant sprocket. The maximum and minimum roller seating angle α is defined as:αmax=140°−(90°/Z) and αmin=120°−(90°/Z)
Chain drive systems have several components of undesirable noise. A major source of roller chain drive noise is the sound generated as a roller leaves the span and collides with the sprocket during meshing. The resultant impact noise is repeated with a frequency generally equal to that of the frequency of the chain meshing with the sprocket. The loudness of the impact noise is a function of the impact energy (EA) that must be absorbed during the meshing process. The meshing impact energy absorbed is related to engine speed, chain mass, and the impact velocity between the chain and the sprocket at the onset of meshing. The impact velocity is affected by the chain-sprocket engagement geometry, of which an engaging flank pressure angle γ (FIG. 2B) is a factor, where:
                    E        A            =                                    w            ⁢                                                  ⁢            P                    2000                ⁢                  V          A          2                      ;                      V        A            =                                    π            ⁢                                                  ⁢            n            ⁢                                                  ⁢            P                    30000                ⁢                                  ⁢                  sin          ⁡                      (                                          360                Z                            +              γ                        )                                ;              γ      =                        180          -          A          -          α                2              ;    and                  EA=Impact Energy [N*m]        VA=Roller Impact Velocity [m/s]        γ=Engaging Flank Pressure Angle        n=Engine Speed [RPM]        w=Chain Mass [Kg/m]        Z=Number of Sprocket Teeth        A=Tooth Angle (360°/Z)        α=Roller Seating Angle        P=Chain Pitch (Chordal Pitch)        
The impact energy (EA) equation presumes the chain drive kinematics will conform generally to a quasi-static analytical model and that the roller-sprocket driving contact will occur at a tangent point TP of the flank and root radii Rf,Ri as the sprocket collects a roller from the span.
As shown in FIG. 2B, the pressure angle γ for an ISO-606 compliant sprocket is defined as the angle between a line L1 extending from the center of the engaging roller 28, when it is contacting the engaging tooth flank at the tangency point TP, through the center of the flank radius Rf, and a line L2 connecting the center of the fully seated roller 28, when it is seated on the root diameter D2, and the center of the next meshing roller 30, as if it were also seated on the root diameter D2 in its engaging tooth space. It should be appreciated that γ is a minimum when α is a maximum.
FIG. 2B also shows the engagement path (phantom rollers) and the driving contact position of roller 28 (solid) as the drive sprocket 12 rotates in the direction of arrow 11. FIG. 2B depicts the theoretical case with chain roller 27 seated on root diameter D2 of a maximum material sprocket with both chain pitch and sprocket chordal pitch equal to theoretical pitch P. The noise occurring at the onset of roller engagement has a radial component FIR as a result of roller 28 colliding with the root surface Ri and a tangential component FIT generated as the same roller 28 collides with the engaging tooth flank at point TP as the roller moves into driving contact. It is believed that the radial impact occurs first, with the tangential impact following nearly simultaneously. Roller impact velocity VA is shown to act through, and is substantially normal to, engaging flank tangent point TP with roller 28 in driving contact at point TP.
Under actual conditions as a result of feature dimensional tolerances, there will normally be a pitch mismatch between the chain and sprocket, with increased mismatch as the components wear in use. This pitch mismatch serves to move the point of meshing impact, with the radial collision still occurring at the root surface Ri but not necessarily at D2. The tangential collision will normally be in the proximity of point TP, but this contact could take place high up on the engaging side of root radius Ri or even radially outward from point TP on the engaging flank radius Rf as a function of the actual chain-sprocket pitch mismatch.